My current materials include the following:
- A backpack (for the straps, and possibly the back fabric section)
- Both tanks, of two different sizes (Think similar to this). The one is made of a 2L pop bottle, the other a thicker energy drink bottle.
- A standard binder (see later)
- Paint, glue, etc.

Okay, my thinking is such:

I can strip the backpack of its back panel, where the straps are attached. I can use the binder to act as a stiff backing, cover it in the backpack fabric and also to possibly adhere the big bottle to..? (I'm not sure how, without breaking things or risking poor craftsmanship). It would have to be fairly hidden.. the game model has a chunk of plastic, from what I can tell, that holds the thing in there, which is sort of what I'm trying to mimic.

Similarly, I need suggestions as to securely adhering both bottles together.

I'm down to the wire here, guys, so I appreciate any and all help!! This costume should hopefully be worn this Saturday (!!) so give me your quick, easy, down and dirty suggestions!

A friend of mine did a medic cosplay last year and, while she had a different pack than you or the standard medic, we still had to attach the pack to her back.
Her's was made out of a large tin (think square cookie tin). We ended up cutting slots into the tin using a dremel I believe. After that we fed the straps through and attached on the inside.
I think something similar could work here. if you can clamp it then you could just use some strong glue (but you would then probably have to attach the straps before you are actually done with the pack).

As for attaching the two bottles together to make a pack, what about something like contact cement?

What colour is the binder? If it's black, I'd say attach it to the backpack backing (maybe use some hot glue or staple gun or something). Then, if you can, get pink insulation foam (ideally) and cut it into two small retangular blocks, as it looks like the bottles attach onto that. Paint it (remember to use gesso and no spray paint!) and then glue to bottles onto that. Finally, glue the whole deal onto the binder. If you can't get insullation foam, just cut some cardboard and paper mache it for a better finish. I guess for the black rings you can just take black bristol board and cut it into strips, then wrap it around the bottles.

A better way to fasten the bottles onto the binder IMO would be to drill some holes in the binder and bottles and use screws with some Loctite on it, but it depends how comfortable you are with power tools.